Does PPP hold for Norway?

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Does PPP hold for Norway?

Einar Wøien Nordbø

¹

Master thesis for the cand.oecon.-degree University of Oslo, Department of Economics

16th December 2004

1Contact information: Work: Forskningsavdelingen, Norges Bank, PB 1179 Sentrum, 0107 Oslo.

Phone: 22316295 E-mail: [email protected].

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List of Figures

2.1 The gold price differential US - UK . . . 9

4.1 The Norwegian REER, I40 . . . 29

4.2 Impulse response graph for I40 . . . 32

4.3 IW(14), TW(14) and CW(14) from 1973 to 2000 . . . 33

4.4 I40 and non-European REERs . . . 37

4.5 The REERSome to 1950 . . . 38

4.6 I40 and major bilateral real exchange rates . . . 41

4.7 The UK-Norwegian real exchange rate, 1819-2003 . . . 42

A.1 Bilateral real exchange rates, 1973 - 2000 . . . 83

A.2 Bilateral real exchange rates, 1973 - 2000 (continued) . . . 84

A.3 Bilateral real exchange rates, 1973 - 2000 (cont.) . . . 85

A.4 Real effective exchange rates, full sample . . . 86

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List of Tables

2.1 The Big Mac Index . . . 8

4.1 Data span necessary to reject H₀ . . . 28

4.2 ADF-equation for the Norwegian REER I40 . . . 31

4.3 Correlation matrix for IW(14), TW(14) and CW(14) . . . 33

4.4 Test results for IW(14), TW(14) and CW(14) . . . 34

4.5 Half-life for TW and CW . . . 34

4.6 Test for REERs from 1973, without a trend . . . 35

4.7 Half-life for REERs from 1973, without a trend . . . 36

4.8 Test results for the UK-Norwegian real exchange rate . . . 42

4.9 Half-life and explanations . . . 45

4.10 Correlation of explanatory variables . . . 46

4.11 Determination of the delay parameter d . . . 50

4.12 Model selection, ESTAR or LSTAR? . . . 51

A.1 Average weights, 1973 to 2000 . . . 73

A.2 REER from 1973, with a trend . . . 74

A.3 REER from full sample, without a trend . . . 75

A.4 REER full sample, with a trend . . . 76

A.5 Bilateral results from 1973 without a trend . . . 77

A.6 Bilateral half-life after 1973 without trend, and data grades . . . 78

A.7 Bilateral results from 1973 with a trend . . . 79

A.8 Bilateral results from 1950, without a trend . . . 80 v

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A.9 Bilateral results from 1950, with a trend . . . 81

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Abstract

This paper is an empirical investigation of whether the theory of purchasing power parity (PPP) describes Norwegian data well. I have used absolute price data from the Penn World Table (PWT) and constructed real effective exchange rates (REER) for Norway against various groups of countries. My main focus is on an importweighted REER against a group of 40 countries. By employing simple unit root tests on this REER over the period from 1973 to 2000 I get strong rejections of the unit root hypothesis, and accordingly, firm support of PPP. The implied half-life of deviations from PPP is less than two years. This is contrary to what some previous PPP studies done on Norwegian data have found. Furthermore, I test for PPP also bilaterally, but I can only detect evidence of PPP against a few countries.

The REERs thus appear to be more stationary than most bilateral real exchange rates.

This feature can be explained if it is the case for Norway that shocks to some bilateral real exchange rates are positive, whereas others simultaneously are negative. In a weighted average of several bilateral real exchange rate - a REER - these shocks may roughly cancel, making the REER more stationary.

Possible explanations for why Norway has exhibited faster mean reversion than many other countries is the policy of nominal exchange rate stability that hase been followed in the post Bretton Woods period, and the coordinated policy attempts at maintaining the competitiveness of the tradable sector that has been done.

In addition, I have tried to identify factors that explain the variability in half-life of deviations from PPP as compared with different countries. I have found that distance, the level of development and the level of bilateral trade are possible explanatory factors.

Looking at nearly two centuries of data I find the Norwegian-UK real exchange rate to be trend stationary. This can be interpreted as evidence of a Balassa-Samuelson variant of PPP,

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as productivity growth - here measured by growth in real gross domestic product (GDP) per capita - on average has been higher in Norway than in the UK in the respective period.

Furthermore, I have tested for nonlinearities in some bilateral real exchange rates for Norway, as nonlinear models have been found to describe some other real exchange rates better than linear models. But the tests I have performed do not indicate any meaningful nonlinearity.

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Abbreviations and acronyms

Abbreviations and acronyms frequently used in this paper are explained here. Most of them are explained the first time they appear in the paper as well, but I have still included this list to make it easier for the reader.

ADF Augmented Dickey-Fuller, a frequently used test for non-stationarity.

ADF-coefficient The level variable coefficient in an ADF regression. The parameter % in equation 2.6.

CW(14) A real effective exchange rate constructed by the competitiveness weights of the OECD. Constructed for comparison. Countries listed in the appendix, section A.4.

CW24 A real effective exchange rate constructed by the competitiveness weights of the OECD. Included countries listed in the appendix, A.4.

DF-GLS Dickey-Fuller, generalized least squares. Another test for non-stationarity.

ESTAR Exponential smooth transition autoregressive, a nonlinear model.

I40 The broadest real effective exchange rate index used in this paper, constructed by import weights. Includes 40 countries. The countries are listed in the appendix, A.4

I44 A nominal effective exchange rate constructed by Norges Bank, using import weights.

See the appendix, A.4.

IFS International Financial Statistics, a database published by the IMF.

IMF International Monetary Fund

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IW(14) An importweighted real effective exchange rate constructed in this paper for comparison purposes. See appendix A.4.

KPSS Kwiatkowski, Phillips, Schmidt and Shin. A test of stationarity.

LSTAR Logistic smooth transition autoregressive, a nonlinear model.

NID Normally, independently distributed.

OECD The Organization for Economic Co-operation and Development.

PP Phillips-Perron, a test for non-stationarity.

PWT Penn World Table.

REER Real effective exchange rate.

s.e. Standard error. The standard errors of the estimated parameters are normally reported in (parentheses) in the tables, to distinguish them from p-values, which are reported in [square brackets].

STAR Smooth transition autoregressive, a family of nonlinear models. ESTAR and LSTAR are two members.

TAR Threshold autoregressive, a nonlinear model.

TW(14) A tradeweighted real effective exchange rate constructed for comparison. The included countries are listed in the appendix, A.4.

TW16 A tradeweighted real effective exchange rate. The included countries are listed in the appendix, A.4.

** Denotes significance at the 1% level. A single * and (*) implies significance at the 5%

and 10% level, respectively, for the results reported in the tables.

hl(ADF) Half life calculated by the simple formula, see section A.2 in the appendix, on the ADF-coefficient. hl(IR) and hl(AR1) denote half-lives based on the impulse response function (IR) and an estimated AR(1) model.

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xi PPP Purchasing power parity.

GDP Gross domestic product.

AIC Akaike information criterion.

MAIC Modified Akaike information criterion.

BIC Bayesian information criterion.

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Preface

This paper was written while I had a student internship in the Research Department at Norges Bank¹ (the central bank of Norway) from June 2004 through November the same year. I would like to express my gratitude to Norges Bank for providing me with economic funding and inspiring working conditions during this period, and above all, for allowing me to write my master thesis about a topic I found interesting. I would in particular like to thank my advisor in Norges Bank, Farooq Akram, who helped me with this paper from the very beginning and gave me a lot of good advice throughout the process. But I am also indebted to Øyvind Eitrheim, Ida Wolden Bache and Lucio Sarno for meaningful discussions and hints along the way. Furthermore, I am grateful to Katrine Godding Boye for allowing me to use some of the data she had gathered. I would also like to thank Maurice Obstfeld and Michael Jansson, both at UC Berkeley, for giving me some advice on relevant literature.

Their classes in international economics and time series analysis, which I followed while I was a visiting student at Berkeley from August 2003 till June 2004, were also the classes that I have benefitted most from when writing this thesis. And finally I must thank my advisor at the University of Oslo, professor Erik Biørn, who read numerous drafts of this paper and helped me detect many mistakes. Without the help and advice from all these people, this paper would definitely have been much worse than it actually is. But all remaining errors are of course my own responsibility.

1The views expressed in this paper are those of the author and not necessarily those of Norges Bank.

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Chapter 1 Introduction

Under the skin of any international economist lies a deep-seated belief in some variant of the PPP theory of the exchange rate.

Dornbusch and Krugman (1976)

The topic of this paper is purchasing power parity - the simple idea that the price levels in different countries should be equal when they are converted to a common currency. The literature on this issue has seen an explosive growth in recent decades, and as argued by Imbs et al. (2005, forthcoming), PPP is perhaps the most intensely researched area in international macroeconomics.

One reason for this is probably that researchers for a long period failed to detect any evidence of PPP at all, and they were thus contradicting a basic assumption in many standard models. As new econometric tools were developed and researchers started using longer time series of data, most studies would be more supportive of PPP, but only as a long run property of the real exchange rate. A consensus was built around an estimated half-life of deviations from PPP on 3 to 5 years. This remarkable persistence of shocks to the real exchange rate combined with the very high short run volatility, led Rogoff (1996) to formulate "the purchasing power parity puzzle". The basic rationale for this puzzle is that the short run volatility is so large that it can only be accounted for by monetary shocks. But if monetary factors were the main source of shocks to the real exchange rate, one would expect that the shocks would die out much faster, as monetary shocks only affects the real economy through

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nominal rigidities in standard models.

There have of course been numerous attempts at explaining this puzzle, and some of them are described in the following chapter. The purpose of this paper is rather to investigate the PPP issue with a basis in Norwegian data. This has been done before, for instance by Bjørnland and Hungnes (2003) and Akram (2005, forthcoming), but no concensus has been reached. This paper differs from the two mentioned above because it uses absolute price data from the Penn World Table, which makes it possible to test also the absolute version of PPP. The Penn World Table is the best attempt so far at determining the price of the same basket of goods across countries, denoted in a common currency.

I have studied PPP by looking at real effective exchange rates against various groups of countries over the post Bretton Woods period, and the broadest group, named I40 here, consists of 40 countries, all included in the I44-index constructed by Norges Bank. But I have also studied PPP bilaterally against the same 40 countries and given an estimate of the speed of convergence to PPP for each country. Furthermore, I have tried to identify factors that can explain the variability in the speed of convergence to PPP. This gives a broader basis for discussing PPP with respect to Norway than in previous studies.

But I have also looked at longer time series, and the longest one is the real exhange rate between Norway and the UK from 1819 to 2003. In addition, I have tested for nonlinear mean reversion in some bilateral real exchange rates, one of the possible solutions to the so-called PPP puzzle that has been put forward.

The majority of the published PPP studies have focused on the relationship between the major international currencies. Norway differs from these economies in several ways. Above all, Norway is a small open economy and is therefore much more influenced by developments abroad than for instance the US. In addition, although Norway is a highly developed country by most standards, its export has a much larger share of non-manufactured goods (mainly oil) than many other developed economies. A related factor is that Norway, through the oil discoveries in the 1970s and the resulting revenue, has been able to finance an extensive public spending. These are some factors that can cause PPP to be a more or less relevant concept for Norway than for other countries - and thus, they provide some reasons for why a PPP study with a basis in Norwegian data can be interesting.

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3 This paper is organized in the following manner. Chapter 2 describes the PPP theory and surveys the empirical literature. I also provide some theoretical considerations for why PPP might fail. In chapter 3 I report the data I have used, how they have been aggregated and the econometric methods I have employed to test for PPP. The 4th chapter contains the empirical results of my studies. Chapter 5 concludes and summarizes the paper.

The econometric software programs I have used in this paper are Eviews 5.0 and PcGive 10.

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Chapter 2 Theory and empirical literature on PPP

2.1 Economic Theory and Concepts

The theory of purchasing power parity is based on the assumption of frictionless goods market arbitrage. When the price of a similar good in two different countries is converted to a common currency, the price should be equal. This is often referred to as thelaw of one price. In mathematical terms, this can be expressed in the following formula for a good i

Pi =EP_i^∗, (2.1)

where P_i is the domestic price of the good, E is the exchange rate, and P_i^∗ is the foreign price. If this condition is violated, economic reasoning suggests that it would be profitable to export the good from the country where it is cheap to where it is expensive. And if prices on a given day differed by a substantial amount, for instance due to a recent devaluation, one would expect them to be equalized by arbitrage as traders take advantage of the difference.

Of course, one may point to a number of reasons for why this condition might fail. Two of the most obvious are transportation costs and tariff barriers. But the idea that changes in the real exchange rate, given by R =EP^∗/P, where P denotes the aggregate price level, should be completely unpredictable, as suggested by Roll (1979), is hard to accept for most economists. Roll argued that the real exchange rate should behave as an asset price if foreign exchange markets are efficient. But as pointed out by Froot and Rogoff (1995), the real exchange rate is not a price of a traded asset. The asset market analogy is therefore

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2.1. ECONOMIC THEORY AND CONCEPTS 5 somewhat faulted.

If the law of one price holds for all commodities it implies thatabsolute purchasing power parity is valid as well. Absolute PPP requires that a given basket of goods and services costs the same in two countries

n

X

i=1

α_iP_i =E

n

X

i=1

α_iP_i^∗,

n

X

i=1

α_i = 1. (2.2)

αi is the weight assigned to the different items in the index. As can be seen, absolute PPP may hold even though individual goods prices differ.

Testing this condition on actual data has proved to be difficult. One problem is lack of comparable data. The construction of a consumer price index is usually a task done by the national statistical authorities, and the method and weights used are therefore countryspe- cific. An additional problem is that consumer price indices are just what they are called, an index relative to a base year. Unless absolute PPP prevailed in the base year, consumer price indices don’t inform us about the magnitude of absolute price deviations from one country to another.

The Penn World Table (Heston, Summers and Aten, 2002) used in this paper is the best attempt so far to circumvent this problem. It contains data on the price in US dollars of a comparable basket of goods for more than 160 countries, stretching back to 1950 for most of them.¹ But the PWT has not been used extensively in tests of PPP. The huge majority of PPP studies have instead concentrated on so-called relative PPP. This condition is satisfied if the relationship between the foreign and domestic price level, measured in a common currency, is constant over time. It is usually not required that the weights in the two indices are equal.

n

X

i=1

αiPit/

n

X

i=1

αiP_it−1 = (Et/E_t−1)(

n^∗

X

i=1

α^∗_iP_it^∗/

n^∗

X

i=1

α^∗_iP_it−1^∗ ). (2.3) The relative version of PPP allows for transportation costs and other obstacles to trade, since the real exchange rate is not required to be equal to one. But this version of PPP cannot be derived directly from the law of one price (Dornbusch, 1985). An alternative

1The Penn Word Table is described in more detail in section A.1 in the appendix.

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theoretical underpinning is the neutrality property of money in the long run, which says that a purely monetary disturbance eventually will result in an equal change in the money stock and all prices, including the exchange rate. The real exchange rate will therefore be unchanged. The belief in PPP is in this respect closely related to the belief that the majority of shocks to the real exchange rate are monetary disturbances.

2.2 The history of PPP

The idea of PPP is not new. The origins of the theory can be traced as far back as to the Salamanca school in 16th century Spain, and classical economists like David Ricardo, John Stuart Mill and Alfred Marshall have all discussed variants of PPP. But the modern version of the theory is attributed to the Swedish economist Gustav Cassel, who was the one who came up with the name "Purchasing Power Parity". He also became a leading protagonist of PPP as a theory of exchange rate determination in the period after World War I, when economists and politicians discussed if and how one should return to the gold standard. Most countries had allowed their currencies to float during the war, and the inflation rates had been widely different from country to country. Cassel proposed using PPP-calculations to find the appropriate level to reinstate gold parities, instead of restoring the prewar parities, as others argued. The influential John Manyard Keynes was among the economists who gave him support, but Cassel’s ideas remained controversial.

PPP reemerged as a relevant theory in the aftermath of World War II, when once again exchange rates had to be reset following a period of no convertibility. An important theoretical innovation came with the work of Balassa (1964) and Samuelson (1964), who predicted that countries that had a relatively more rapid productivity growth in the tradable sector would experience a real appreciation of the currency.²

The monetary theory of the exchange rate, which was popular in the early 1970s,³ had as a key assumption that purchasing power parity held at all times. But the downfall of the Bretton Woods system in 1973 led to an unprecedented degree of real exchange rate volatility, and the deviations from PPP were both large and persistent. A number of empirical studies

2See section 2.4 for a more detailed description of the Balassa-Samuelson effect.

3See Frenkel and Johnson (1976) for more on the monetary theory of the exchange rate.

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2.3. EMPIRICAL WORK ON PPP 7 were even unable to reject the hypothesis of the real exchange rate as a random walk. More recent work have been more supportive of PPP as a long-run property of the real exchange rate, and as Taylor and Taylor (2004) note in their recent survey of the PPP literature:

In this respect, the idea of long-run PPP now enjoys perhaps its strongest support in more than thirty years, a distinct reversion in economic thought.

The empirical work on PPP will be explored more closely in the following section.

2.3 Empirical work on PPP

2.3.1 The law of one price

Although the idea of purchasing power parity sounds plausible, the most striking aspect of the empirical literature on PPP is probably how large and persistent the deviations can actually be. A famous example of deviations from the law of one prize is the "Big Mac index" published by the magazine "The Economist", see table 2.1. A Big Mac hamburger in different countries is very close to being a homogenous good, but in spite of this, the most expensive burger in the sample, the one you find in Iceland, costs almost five times as much as the cheapest one, which is sold in the Philippines. But the large deviations are not that difficult to understand once you consider the huge nontraded components of the price of a Big Mac, like ingredients bought locally, wages to the salespeople and property rental costs.

In an entertaining paper Cumby (1996) finds that once you correct for average deviations, that is, use the "Big Mac index" as a measure of relative PPP, the index is actually a pretty good indicator of future exchange rate changes. Half-life⁴ of deviations from "Big Mac- parity" is found to be about one year, far below the consensus half-life estimate of 3-5 years in the literature.

But the law of one price applies to some markets. Figure 2.1 shows the market price differential for one ounce fine gold in New York and London, measured in US dollars, in percentage of the London price for every year from 1791 to 1998. The biggest price difference is 13 percent, recorded just after World War II.⁵ The average deviation, in absolute value,

4The time it takes before the effect of a unit innovation is halved, see section A.2 in the appendix

5The data are gathered from Officer (2001, 2002).

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Table 2.1: The Big Mac Index Country Big Mac price

United States 2.90

Argentina 1.48

Australia 2.27

Brazil 1.70

UK 3.37

Canada 2.33

Chile 2.18

China 1.26

Czech Rep. 2.13

Denmark 4.46

Euro area 3.28

Hong Kong 1.54

Hungary 2.52

Iceland 6.01

Indonesia 1.77

Japan 2.33

Malaysia 1.33

Mexico 2.08

Norway 5.18

Philippines 1.23

Poland 1.63

Russia 1.45

Singapore 1.92

South Africa 1.86

South Korea 2.72

Sweden 3.94

Switzerland 4.90

Taiwan 2.24

Thailand 1.45

Turkey 2.58

Venezuela 1.48

Prices of a Big Mac in current US dollars. Source: Economist.com, May 27th 2004.

is 1,6 percent, and the median deviation 0,6 percent. The average deviation is somewhat higher before 1900 compared to after 1900, 2,0 percent versus 1,2 percent.

In a frequently cited study on the law of one price, Engel and Rogers (1996) investigate relative price differences between US and Canadian cities. They find that both whether the cities are located on different sides of the border and the distance between them help explain the deviations. But just crossing the border in itself has a substantial impact on the

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2.3. EMPIRICAL WORK ON PPP 9 Figure 2.1: The gold price differential US - UK

1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890

−10

−5 0 5 10

Percentage deviation

1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

−10

−5 0 5 10

Percentage deviation

The difference in the gold price in current US dollars in New York and London, in percentage of the London price. I have annual data from the period 1791 to 1998.

volatility of the price differential between two cities. It is equivalent to a distance of 75 000 miles, according to one of their calculations.

In another study of the law of one price, Froot, Kim and Rogoff (1995) challenge the conventional belief that the high volatility of relative prices is a characteristic of the modern period of floating exchange rates only. Looking at annual commodity price data spanning seven centuries for England and Holland, they find that the volatility and the persistence of deviations from the law of one price have been relatively stable over time.

These are only two of a large number of studies that question the applicability of the law of one price. Given the weak empirical support for the basic building block of the PPP

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theory, it should not come as a surprise that researchers have had problems with producing strong evidence in favour of PPP also on the aggregate level.

2.3.2 PPP on the aggregate level

I will divide the empirical literature on PPP into four groups. More extensive surveys are given in Froot and Rogoff (1995), Rogoff (1996), Sarno and Taylor (2002) and Taylor and Taylor (2004). This survey is inspired by all the surveys mentioned, but draws most heavily on Froot and Rogoff (1995).

In what I will refer to as the first group in the empirical PPP literature, consisting of the early tests, the null hypothesis is that PPP holds. One early study that was supportive of PPP, was done by Frenkel (1978). He ran the following regression,⁶

et=α+β(pt−p^∗_t) +εt, (2.4) on data from several hyperinflationary economies, and he found estimates of the coefficient β close to one, which he interpreted in favour of PPP.⁷ But most of the other early studies were not supportive of PPP. A general problem with these studies was the lack of adequate econometric techniques. Today we know that if the error term in (2.4) is integrated of order one, I(1),⁸ the standard OLS test of β= 1 is invalid.⁹

The second group of studies, where the null hypothesis is that the real exchange rate is a random walk, takes advantage of the work by Dickey and Fuller (1979) and others in developing a valid test procedure for regressions containing a unit root. One example of a

6Throughout, lowercase letters denote natural logs.

7Ifβ is equal to one, it implies that the real exchange rate will be equal to constant, which is equivalent with the relative version of PPP. Absolute PPP would prevail if the constant equaled zero, given that you have absolute price data and the same basket of goods.

8As it would be if the autoregressive operatorψ(L)in the following expression,

(1−φ1L−φ2L²−. . .−φpL^p)εt≡ψ(L)εt=ut, (2.5)

has a unit root, where ut is white noise. This implies that the series does not have constant mean and variance.

9For a good introduction to regressions containing a unit root, see Hamilton (1994), chapter 17. A more advanced treatment is given in Stock (1994).

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2.3. EMPIRICAL WORK ON PPP 11 paper where this approach is used is Meese and Rogoff (1988). The authors cannot reject the null hypothesis of the real exchange rate being integrated of order one for dollar-mark, dollar-sterling and dollar-yen series over the post Bretton Woods period. Meese and Rogoff use a so-called augmented Dickey-Fuller (ADF) test, with the following specification

∆r_t =µ+ (%−1)r_t−1 +

k

X

i=1

ψ_i∆r_t−i+ε_t, (2.6)

where r_t is the log of the real exchange rate.

Given the low power of the unit root test, it is not surprising that Meese and Rogoff and others who employed similar tests failed to find evidence of PPP.¹⁰ Alternative tests using variance ratios and tests of fractional integration were performed with the same depressing results for the PPP advocates.

The profession has followed two different paths in trying to resolve the problem of low power. One solution has been to extend the sample period. Frankel (1986) used data on the dollar-sterling real exchange rate from 1869 to 1984, and was able to reject a random walk. His half-life estimate was 4,6 years. Johnson (1990) also found support of PPP using cointegration methods on 120 years of US/Canadian real exchange rate data. Edison and Klovland (1987) looked at annual data from Norway and the UK spanning the period from 1874 to 1971 and detected evidence in favour of long-run PPP if they allowed for different short run dynamics during the floating period from 1914 to 1928.

An obvious problem with these studies is that they span periods with varying exchange rate regimes. It is well documented that the real exchange rate variability tends to be higher during periods with a floating exchange rate (see Mussa, 1986). Lothian and Taylor (1996) investigate the implications this has for studies using long data sets. Using sterling-dollar and sterling-franc data spanning two centuries, they cannot reject the hypothesis of no structural change before and after Bretton Woods. This indicates that running regressions on data from periods with different exchange rate regimes may be a valid procedure, but it is nevertheless a potential source of misleading conclusions. Another concern with these studies was raised

10In section 4.2 I assume that the true process is AR(1) and use the asymptotic variance of the dependent variable to calculate how many years of data which are necessary to reject the null hypothesis with a standard Dickey-Fuller t-test. If the true half-life is one year, 25 years of data are necessary, for instance.

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by Froot and Rogoff (1995). Since the countries where the long run data series are easiest available, tend to have been continuously among the world’s most developed, these studies might exaggerate the evidence of long run PPP. This concern is particularly relevant if the Balassa-Samuelson effect is true.

The second approach to solve the problem of low power has been to extend the number of observations by using data from more than one country for the post Bretton Woods period.

But many papers within this strand of the literature suffer from a serious weakness, as pointed out by Sarno and Taylor (2002). If a unit root test using panel data results in a rejection of the null hypothesis of a random walk, the only valid conclusion is that at least one of the series used is stationary. One cannot infer from this that PPP holds in general.

One example of a study employing this procedure is Abuaf and Jorion (1990). They use real exchange rate data for ten countries versus the US over the period from 1973 to 1987, and are able to reject the null hypothesis of joint nonstationarity, but only at a significance level of ten percent. Their estimated half-life of deviations is between 3 and 5 years.

Most of the studies in the second group employed univariate test statistics to investigate the PPP issue. In what I will refer to as the third group of the literature on PPP, the more modern method of cointegration is used, taking advantage of the work of Engle and Granger (1987).

The basic idea that warrants the use of cointegration techniques in PPP studies is the belief that the exchange ratee_tand the price differentialp^∗_t−ptboth are I(1), but that a linear combination of them is stationary. If this is the case, we say that the series are cointegrated.

The null hypothesis in these types of studies is therefore that no linear combination of the exchange rate, the foreign and the domestic price level is stationary

et−βpt+β^∗p^∗_t. (2.7)

The only difference from the simple unit root tests is that I there imposed the restrictions β =β^∗ = 1 beforehand and checked for stationarity of the real exchange rate

r_t =e_t−p_t+p^∗_t. (2.8)

An important principle in econometric testing is that one should test a theory, not just

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2.3. EMPIRICAL WORK ON PPP 13 run random regressions. By allowing the coefficients in (2.7) to be different from one, the researcher should have a clear idea of why they might differ. If the series turn out to be cointegrated, but the coefficient estimates differ clearly from one, without any plausible economic explanation, the researcher cannot really claim to have found evidence of PPP.

Some theoretical considerations for why the coefficients might be different from one is provided by Taylor (1988). He constructs models with transportation costs and measurement error and shows that this might give coefficients different from one. His study is among the first to apply cointegration methods to the PPP theory, but he is unable to reject the null hypothesis of no cointegration for any of the country pairs he considers.

Later studies using cointegration methods have been more supportive of PPP, but the estimates of β and β^∗ vary wildly and it is very hard to provide any theoretical explanation for why this should be the case. One potential source of the strange estimates is small sample bias, which has been known as a potentially substantial problem in cointegration studies since the work of Banerjee et al. (1986).

In what I will refer to as the fourth group of PPP test, nonlinear estimation techniques are applied. This is because economic reasoning suggests that real exchange rate dynamics may be described better with a nonlinear model. Transportation costs, tariffs and other barriers to trade have been mentioned before as possible explanations for deviations from the law of one price. Although prices measured in a common currency differ, the marginal profit of shipping goods between the countries might be less than the cost. In this respect the relative prices in the two countries can be disconnected. But if the price deviations become large enough, it will be profitable to ship goods, and the price differences should be reduced.

Obstfeld and Taylor (1997) find evidence of this effect using a threshold autoregressive model (TAR) on disaggregated price data. The idea underlying the use of this particular model is that relative prices may be nonstationary within a band, but that it becomes a mean reverting process once it crosses one of the thresholds.

Other reasons for why the adjustment process might be nonlinear have also been presented. Kilian and Taylor (2003) suggest that heterogeneous opinions in the foreign exchange market about the equilibrium level of the nominal exchange rate might create nonlinearities, and Taylor (2004) argues that the intervention operations of central banks can have the same

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effect. The literature on nonlinearities is explored further in section 4.5.

2.4 Should PPP hold?

The large number of studies that documented substantial deviations from PPP and only provided empirical support of PPP in the very long run, have led economists to come up with various suggestions for why this might be the case. Before I start examining the different theories trying to explain the deviations from PPP, it might be useful to rewrite the basic PPP equation in order to understand where the deviations might come from. The expression for the real exchange rate in natural logs was given in (2.8). Bothp^∗ andpare national price indices consisting of both tradable and nontradable goods. Assuming that the weights are equal in both countries (although differing weights may also be a source of PPP deviations), I obtain the following, where subscripts N and T denote nontradable and tradable goods, respectively

p=αp_T + (1−α)p_N (2.9)

and

p^∗ =αp^∗_T + (1−α)p^∗_N. (2.10) Inserting these two expressions into equation (2.8), I obtain the following expression for the real exchange rate. The time subscripts have been dropped for simplicity

r =α(e+p^∗_T −pT) + (1−α)(e+p^∗_N −pN). (2.11) Since the real exchange rate here is on log form, absolute PPP requires that r= 0, whereas relative PPP holds if the real exchange rate is equal to a constant. If I make the unrealistic assumption that the law of one price holds for tradables, implying that(e+p^∗_T−pT) = 0, we notice that we may still have deviations from PPP if the price of nontradables differ. The matter is further complicated by the fact that most goods that are highly tradable, will have a significant nontradable component.

The most famous theory explaining why the price of nontradables might differ, is the

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2.4. SHOULD PPP HOLD? 15 Balassa-Samuelson effect. I will not derive the theory formally here,¹¹ but only explain its main features in words.

The model underlying the theory assumes that you are looking at a small open economy producing only two goods, one tradable and one nontradable. The law of one price is assumed to hold for tradables, and also the nontradable goods markets are perfectly competitive. The production function exhibits constant returns to scale in the two input factors, capital and labour. Capital is mobile between sectors and internationally, which implies that the real interest rate is determined on the world market. Labour is mobile between sectors, but not across borders. This means that the wage will be the same in both sectors, but can vary internationally.

The key prediction of the model is that a country will experience a real appreciation compared with another country if its productivity growth advantage in the tradable sector exceeds its productivity growth advantage in the nontradable sector. This is conditional on the plausible assumption that the nontradable sector is labour intensive, i.e., labour’s share of the income generated is at least as high in the nontradable as in the tradable sector. That the productivity growth advantage is relatively higher in the tradable sector is reasonable given that the nontradable sector contains most of the service industries (e.g. haircuts).

And if the nontradable sector is labour intensive, you may see a real appreciation even if the productivity growth advantage in the two sectors are balanced.

To provide some economic intuition for the model, let us start in the tradable sector.

For simplicity I assume that the exchange rate is fixed, and that all economic variables in the two countries initially are identical. Since the law of one price holds, the price of the tradable good will continuously be the same in both countries. Without loss of generality, I can assume that the tradable price stays fixed. In the country where the productivity growth in the tradable sector is higher, a larger part of the tradable price will then go to the workers as wages. Since the wage level by assumption must be the same in both sectors, this means that the country with the productivity growth advantage in the tradable sector will pay its workers in the nontradable sector relatively better. And since the productivity growth in the nontradable sector has been smaller, prices here must increase, which results

11For a formal derivation, see for instance Obstfeld and Rogoff (1996), pp. 204–214.

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in a general price increase and a real appreciation of the currency.

The empirical support for the Balassa-Samuelson effect is somewhat mixed, though. The theory works very well for Japan, but studies done on other countries draw a less clear-cut picture. Since the countries that have enjoyed a relative productivity growth advantage in the tradable sector will be relatively richer, one way to test for the Balassa-Samuelson effect is to run a regression on the relationship between the price level and income. This is was first done by Balassa (1964) himself for twelve industrial countries in 1960, and he identified a positive relationship that was clearly significant. Other studies have been less supportive.

Froot and Rogoff (1991a,1991b) detect only weak correlations, at best, between productivity differentials and the real exchange rate for 22 OECD countries. But Edison and Klovland (1987) are able to find some evidence of a Balassa-Samuelson effect by using long run data for Norway and the United Kingdom. More support is offered by Heston, Nuxoll and Summers (1994), who run a number of regressions using the absolute price data in the Penn World Table. As mentioned before, this is also the data set I am going to use.

The Balassa-Samuelson effect may be the most prominent theory explaining long run deviations from PPP, but numerous other explanations have been put forward. A related theory, which also predicts that richer countries will have a more appreciated real exchange rate, was developed by Kravis and Lipsey (1983) and Bhagwati (1984). Instead of looking at productivity differences, they relax the assumption of perfect international capital mobility.

In their model richer countries accumulate more capital per worker, which gives a higher wage level, and a higher price level of nontradables if these goods are labour intensive.

The level of government spending has also been found to explain deviations from PPP.

One explanation is that government spending tends to fall more heavily on nontraded goods, and thereby increase their relative price. Both Froot and Rogoff (1991a) and De Gregorio, Giovanni and Wolf (1994) detect government spending as a significant factor in determining the real exchange rate. The effects die out in the long run, but very slowly, with a half-life of more than five years.

Another explanation that is often mentioned is that sustained current account deficits are closely related to long run real exchange rate depreciation. Obstfeld and Rogoff (1995)

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2.4. SHOULD PPP HOLD? 17 find some evidence of this. One possible explanation is that¹² current account deficits imply wealth transfers from one country to another, and home and foreign residents may have different consumption patterns.

All of the theories mentioned above seek to explain deviations from PPP assuming that the law of one price holds for tradeables. But as the empirical work has shown, deviations from the law of one price can be both large and persistent. Some of the reasons for this are obvious, like transportation costs and tariff barriers. Even for highly traded goods, a significant amount of the price can be due to nontraded components, as previously discussed.

And non-tariff barriers, such as import licensing requirements, technical product standards, anti-dumping duties and so on, may be more important than previously thought.¹³ Knetter (1994) do for instance argue that non-tariff barriers is a very relevant factor in explaining high retail prices in Japan.

At a more advanced level, there are two, not mutually excluding, explanations for why the law of one price might fail. "Pricing to market" is one of them. The name was coined by Krugman (1987), and denotes the ability of producers with market power to charge a different price for the same good in various markets. The car industry is often mentioned as an industry where "pricing to market" is particularly relevant. In a world with perfect competition agents could make profits on the price differences across countries, but this is not possible since the producers can separately license the sale of goods in the different countries.

The other approach to explain why a company may charge different prices for the same good in varying countries is offered by Kasa (1992). Instead of focusing on oligopolistic competition, he stresses adjustment costs. It might be costly for the firms to change prices, that is, they face menu costs, or it might be the consumers who face fixed costs in switch- ing between products. In any case, the adjustment cost story provides an alternative to Krugman’s rationale for "pricing to market".¹⁴ But as mentioned above, both these theories might be useful to understand what the true process is really like.

12Advocated by Krugman (1990).

13It is not unlikely that their importance may have grown after international trade liberalization now has reduced traditional obstacles to trade.

14But this story can of course not explain long run price deviations.

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Chapter 3 Data and method

3.1 Absolute price data

As mentioned earlier, the data set I am going to use in this paper is the Penn World Table.

This data set is discussed more closely in the appendix, section A.1. For a more thorough description of the data and how they have been produced, see Summers and Heston (1991).

As I also indicated, this data set has not been used extensively in tests of PPP. I am only aware of three studies employing the PWT data - Oh (1996), Parsley and Popper (2001) and Zussman (2002).

One of the reasons for this is probably concern with the quality of the data. As em- phasized by Sarno and Taylor (2002), the PWT data are constructed both by interpolations between benchmark years, and extrapolations to countries where no benchmark studies have been done. Because of this they claim that the PWT data become "partially artificial".

I find their concern to be somewhat exaggerated. The interpolations between benchmark years are based on national price indices, and it is difficult to see that the difference between using the indices alone and absolute price data based on the indices can be that important. In addition, by using the PWT data, I gain the advantage that I compare prices on the same basket of goods across countries, which is necessary for tests of absolute PPP. The same method has been applied to construct a price index for every country, whereas national statistical authorities use varying methods. By using PWT data I avoid potential problems related to this. Zussman (2002) uses both data from the PWT and data from the Interna-

18

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3.2. REAL EFFECTIVE EXCHANGE RATES 19 tional Monetary Fund’s (IMF) International Financial Statistics (IFS) database. His results are the same irrespective of which of the two data sources he uses. Another advantage with the PWT is that it has price data for more countries and longer time periods than other data sources. These arguments provide some reasons for why it might be interesting to test PPP by using PWT data.

But more concerns can be raised. One of them is that the PWT only contains annual data. The frequency of the observations does not influence the asymptotic power of the test,¹ but a higher frequency might improve the estimation of short run dynamics of the real exchange rate. But annual data are likely to be time averages - not end of period values, and Taylor (2001) shows that this will bias the coefficient estimate in an AR(1) model upwards.

As a result, the half-life estimate will be biased upwards as well. Taylor (2001) argues that this feature might be one solution to the so-called PPP puzzle (Rogoff, 1996).² More recently, Imbs et al. (2005, forthcoming) have argued that aggregation across sectors may also cause an upward bias in the half-life estimates. But their work is challenged by Chen and Engel (2004).

On the other hand it has been known at least since the work of Orcutt (1948) that the OLS estimate of an AR(1) coefficient will be biased downwards. Median unbiased estimators that take this into account have been developed,³ but just correcting for one type of bias when there are likely to be several can be misleading. In this case, for instance, it is not impossible that the different sources of bias will cancel. My approach will instead be to use standard methods and be aware of the potential biases when interpreting the results.

3.2 Real effective exchange rates

Another special feature with this study is that I have constructed real effective exchange rates (REER), that is, a weighted average of a number of bilateral real exchange rates.⁴

1I have discussed this in more detail in section 4.2.

2Zussman (2002) finds some evidence of this effect. Using annual, quarterly and monthly data from the same countries, he finds that the half-life estimates are higher the lower frequency of the data.

3See Cashin and McDermott (2003) for a study of PPP where such a method is applied.

4For a mathematical expression of a REER, see equation 3.2 and 3.3.

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The huge majority of the PPP studies that have been done have instead chosen to focus exclusively on bilateral real exchange rates. The drawback with using REERs is that all the bilateral real exchange rates can be I(1), but a linear combination of them may for some reason be stationary, or cointegrated.⁵ If a REER is found to be stationary, one cannot really claim to have found evidence of PPP.

On the other hand, for policy purposes, and in particular for an institution like the central bank of Norway, the most interesting variable is in fact the real effective exchange rate. If there is a tendency for the REER to revert to its mean over time, this is a relevant result for monetary policy purposes, even though it is debatable whether you can refer to it as PPP or not.

Another way to warrant the use of REERs is to imagine that the world only consisted of two countries - home and abroad. This is a frequent assumption in open economy models.

Investigating the idea of PPP in such a setting necessitates the construction of a real effective exchange rate. The exercise would in any case not be that much different from what is done when studying the real exchange rate against the euro area these days. The exchange rate is the same in all countries, but when constructing price data, it will be a weighted average of price data from the euro members. This is in principle similar to what I do when I construct a weighted real exchange rate, with weights corresponding the countries’ importance for Norway.

In any case I will also do a number of regressions on bilateral data.

The real exchange rate as compared with country i in a given year t is by definition given by

R_it= P_it^f

P_t^h, (3.1)

whereP_it^f is the price level in the foreign country andP_t^h the price level in the home country (Norway). This formula differs from the one introduced in section 2.1 because it assumes that the price levels are denoted in a common currency, which is the case in the Penn World Table. All price levels are expressed relative to the US price level in the current year and denoted in US dollars.

5I would like to thank Lucio Sarno for pointing this out to me.

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3.2. REAL EFFECTIVE EXCHANGE RATES 21 The real effective exchange rate is constructed by Laspeyres’ index formula. This formula is also used by the IMF and Norges Bank, among others, when constructing (real) effective exchange rates.

The real effective exchange rate in year t is given by

R_t=

n

Y

i=1

R_it^W^it, where

n

X

i=1

W_it= 1. (3.2)

In logs the same equation becomes

r_t =

n

X

i=1

W_itr_it. (3.3)

The choice of weights may clearly influence the results. The optimal weights in the construction of a real effective exchange rate should correspond to the relative impact the respective countries have on the Norwegian economy. One argument for using import weights is that Norway is a small open economy, and that the majority of impulses from abroad come in the form of imported inflation. On the other hand, in order to maintain international competitiveness for the tradeable sector, this sector has traditionally played a leading role in the wage bargaining process in Norway. So even if Norway as a small open economy has no influence on prices abroad, it is not unlikely that developments in the most important export markets can have an impact on Norway. This warrants the use of trade weights instead of import weights.⁶

If export and import is relatively balanced versus most countries, this concern is super- fluous. A quick inspection of the trade and import weights,⁷ shows that the different weights are quite similar for most countries in most years, but that there are some exceptions. For instance, the weight assigned to the United Kingdom will in general be much higher if I use data on total trade instead of only import data.

But using trade data can also be criticized for being a too simplistic approach. Two

6The data that the trade and import weights are based on was obtained from Statistics Norway. The data are in current value in Norwegian kroner. The weight assigned to a specific country is the value of the import (trade) from (with) that country that year divided by the value of import (trade) from (with) all the countries in the respective group.

7The average weights over the post Bretton Woods period are reported in the appendix, table A.1.

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countries that export the same type of commodities may not engage in an extensive, bilateral trade. But impulses from one of the countries are likely to be important for the other. This will not be captured by trade or import weights. The composition of a country’s trade can also matter. If a country only exports goods that are priced on the world market, one would want to give it less weight than a country where the exporting firms enjoy some market power ("pricing to market").

These concerns have led to the development of far more sophisticated weighting measures.

The IMF and the OECD have both constructed so-called competitiveness weights which are used in the construction of nominal and real effective exchange rates. These weights take the composition of the total trade into account and also include a measure of competition in third markets - not just bilateral trade flows.⁸

My main focus will nevertheless be on an importweighted real effective exchange rate.

This is partially due to the fact that import weights were easiest available. In addition, even if the development in the most important export markets does matter, the impulses from the import markets are likely to be more consequential. But to check the robustness of my results, I have also constructed real effective exchange rates using total trade weights and the competitiveness weights of the OECD.

3.3 Econometric method and model

My null hypothesis will be that the real (effective) exchange rate is I(1). A rejection of the null will be interpreted as evidence in favour of PPP. Of course, that the real (effective) exchange rate is not I(1) is only a necessary condition for PPP. But since univariate regressions on single country data from the post Bretton Woods period generally have failed to reject the null hypothesis, I find this approach interesting enough.

Absolute PPP implies that the log of the real exchange rate has zero mean, since I have absolute price data here. As discussed in section 2.4, there are a number of reasons for why this condition might fail. Therefore, I will allow for a constant term. Rejection of the null

8A more detailed description and discussion of the IMF procedure is given in Zanello and Desruelle (1997).

The OECD procedure is presented in Durand, Simon and Webb (1992).

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3.3. ECONOMETRIC METHOD AND MODEL 23 hypothesis with a constant term significantly different from zero indicates that relative PPP holds. But I will generally not allow for a deterministic trend. Some authors argue that a real exchange rate model including a deterministic trend can be interpreted as a test of the Balassa-Samuelson modified version of PPP,⁹ but it is not obvious that a deterministic trend is a good description of a process of relative productivity growth.

Another question is which testing procedure to apply to test for a unit root. A large number of different test statistics have been proposed, and, as discussed by Stock (1994), it is an inherent problem in unit root testing that it doesn’t exist a univariate most powerful test of the autoregressive parameter being equal to 1 versus being less than 1 in a simple AR(1) model. Size and power vary substantially between different test statistics, and in addition, the properties of the test statistics can be very sensitive to the true nature of the model.

Faced with these difficulties I have chosen to employ the most frequently used test statistic, the augmented Dickey-Fuller t-statistic. This is an extension to account for serial correlation in the error terms of the traditional Dickey-Fuller test. But to give an indication of the robustness of the results, I will also report results from other test statistics. Monte Carlo simulations done by Stock (1994) indicate that the ADF t-statistic is good in terms of size, but that this comes at the cost of low power. The ADF t-test is a test of %= 1 versus

% <1in (2.6).

An obvious problem is the choice of the number of lags k, and unfortunately, the results show that whether I can reject the null hypothesis or not is highly dependent on the number of lags included in the regression. Including too few may distort the size of the test, whereas including too many genereally reduces power (Ng and Perron, 1995)).

Numerous procedures have been proposed to select the appropriate number of lags. They range from deterministic rules that relate k to the number of observations¹⁰to data dependent methods that take sample information into account. An example of the latter is the Akaike information criterion (AIC), which is often reported automatically by econometric software programs.

9One example is Papell and Prodan (2004).

10An often used rule,k=integer part of(12×(T /100)^0,25), is due to Schwert (1989).

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Simulation studies exploring the finite sample properties of the varying procedures are conducted by Hall (1994) and Ng and Perron (1995). They both find that the data dependent methods dominate the deterministic rules. Ng and Perron (1995) recommend a general to specific procedure with sequential F- or t-tests of the last lag(s) until the last lag(s) is found to be significantly different from zero. This is a valid procedure as long as the initial number of lags is chosen high enough. Data dependent selection rules such as the Bayesian information criterion (BIC) and AIC perform particularly poor when the true process contains a large, negative moving average component. The same authors (Ng and Perron, 2001) have later come up with a new testing procedure and an information criterion that performs better in unit root test, a modified AIC (MAIC). But since I am going to do a large number of regressions in this paper, I have decided to stick with sequential t-tests, since this approach is very simple to apply in PcGive 10, the program I used in the ADF regressions.

I have started with 4 lags for data series beginning in the 1950s (k = 4), 3 lags for series from the 1960s and 2 lags for series from the 1970s, and then eliminated lags until the last lag was found to be significant. This choice of the maximum number of lags might seem somewhat arbitrary, but because of the limited number of observations, I reasoned that I could not afford to lose more than two observations in the post Bretton Woods period.

Anyway, it is only in a very few cases more than one lag is significant.

The other tests I have applied are the Phillips-Perron test (PP), due to Phillips and Perron (1988), the DF-GLS test developed by Elliott, Rothenberg and Stock (1996), and the KPSS test (Kwiatkowski et al., 1992). All these tests have been done using the econometrics program Eviews 5.0.

The PP test is, as the ADF test, designed to account for serial correlation in the residuals.

But instead of adding lags in the initial regression equation, Phillips and Perron suggested to ignore the serial correlation and estimate the relation by OLS as an AR(1) model. This can be done since the OLS-estimate of the AR(1) coefficient is superconsistent¹¹ under the null hypothesis. They then proposed to modify the test statistic to account for the serial correlation.¹² Several procedures can be applied to do this. I have chosen to estimate the

11Converges in probability to the true value at a faster rate than required for consistency. See Hamilton (1994, p. 460).

12For a more pedagogical and detailed treatment of this test procedure, see for instance Hamilton (1994,

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3.3. ECONOMETRIC METHOD AND MODEL 25

"correction factor" by using the Bartlett kernel, which is the standard procedure incorporated in the econometrics program Eviews 5.0. Unfortunately, one has to choose a bandwidth parameter exogenously for this estimator, and as with the choice of lags in the ADF-case, this choice can be decisive for the test conclusions, especially in small samples. I have chosen the bandwidth parameter by employing a data dependent rule due to Newey and West (1994), which is automatically computed in Eviews.

A third unit root test, which has been found to have both good size and power, is the DF-GLS test. This test is a modified version of the ADF test, and it involves two steps.

First, the explained variable is regressed on a constant (and a trend, if that is included in the model), and then the usual ADF-procedure is run on the demeaned (or detrended) data, the residuals from the preceding regression. This procedure has been found to improve the asymptotic power of the test significantly in the presence of a unknown trend or constant, and simulation results show that the DF-GLS test performs well in small samples as well.¹³ To determine the lag length in the DF-GLS tests I have used the MAIC, introduced by Ng and Perron (2001). This is automatically done in Eviews 5.0.

The fourth test procedure I have employed, the KPSS test, takes a different approach.

The null hypothesis of this test is that the series is stationary - not non-stationary, as above.

I will give a very simple example just to illustrate. A test of stationarity will be a test of the parameter θ = 1 versus θ <1 in the following model

(1−L)rt= (1−θL)εt, εt ∼N ID(0, σ²). (3.4) Whenθ = 1, there is a common factor in (1−L)r_tand(1−θL)ε_t, and r_tis stationary. Since existing unit root test all have flaws, it is often recommended to do stationarity tests as well, to get a cross-check of the results. I have therefore performed KPSS-tests on all regressions where there were significant rejection of the null hypothesis. Results are reported in the respective tables. As with the Phillips-Perron test, this test statistic requires a choice of the bandwidth parameter. I have also here employed the Newey-West bandwidth with the Bartlett kernel, which is automatically done in Eviews 5.0.

chapter 17.6)

13For Monte Carlo results, see Elliott, Rothenberg and Stock (1996)

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Chapter 4 Empirical results

This chapter presents the empirical results of this paper. In the first section I provide a quick overview of the results from some other PPP studies done on Norwegian data. In the second section, I investigate the power properties of the DF t-statistic further, because some of the failures to detect evidence of PPP may be due to insufficient power. The third section contains estimation results for real effective exchange rates versus varying groups of countries. In the fourth section I look at several bilateral real exchange rates, including a series against the UK spanning almost two centuries. I also try to identify factors that can explain the variability in the persistence of deviations from PPP, measured against different countries. In the fifth and final section I try to check whether the real exchange rate is better described by a nonlinear model.

4.1 Previous studies

Earlier tests of PPP that have been done on Norwegian data have given mixed results. Bjørn- land and Hungnes (2003), Chortareas and Driver (2001), Papell (1997) and Alexius (2001) all fail to reject the null hypothesis of the real exchange being I(1) at normal significance levels. But it deserves to be mentioned that most of these studies were done on short data sets, Bjørnland and Hungnes (2003), for instance, have data spanning 17 years only. Both Papell (1997) and Chortareas and Driver (2001) restrict their attention to the bilateral real exchange rate versus the United States.

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Does PPP hold for Norway?